Higher order turän inequalities

The celebrated Turân inequalities P 2 n(x)-P n-x(x)P n+1(x) ≥ 0, x ε[-1,1], n ≥ 1, where P n(x) denotes the Legendre polynomial of degree n, are extended to inequalities for sums of products of four classical orthogonal polynomials. The proof is based on an extension of the inequalities γ 2 n - γ n-1γ n+1 ≥ 0, n ≥ 1, which hold for the Maclaurin coefficients of the real entire function ψ in the Laguerre-Pölya class, ψ(x) = ∑ ∞ n=0 γ nx n / n!. ©1998 American Mathematical Society.

Sharp Turán inequalities via very hyperbolic polynomials

We present new sharp inequalities for the Maclaurin coefficients of an entire function from the Laguerre-Pólya class. They are obtained by a new technique involving the so-called very hyperbolic polynomials. The results may be considered as extensions of the classical Turán inequalities. © 2010 Elsevier Inc.

Higher order turán inequalities for the Riemann ξ-function

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Derivation and consistency of the partial functions of the ternary system involving interaction coefficients

The logarithm of activity coefficients of the components of the ternary system is derived based on the Maclaurin infinite series, which is expressed in terms of the integral property of the system and subjected to appropriate boundary conditions. The derivation of the functions involves extensive summation of various infinite series pertaining to the first-order interaction coefficients that have been shown completely to remove any truncational error. Since the conventional equations involving interaction coefficients are internally inconsistent, a consistent form of the partial functions is developed in the article using the technique just described. The thermodynamic consistency of the functions based on the Maxwell and the Gibbs-Duhem relations has been established. The derived values of the logarithmic activity coefficients of the components have been found to be in agreement with the thermodynamic data of the Fe-Cr-Ni system at 1873 K and have been found to be independent of the compositional paths.

Contemporary New Zealand coefficients for the Trauma Injury Severity Score: TRISS(NZ)

Aims – To develop local contemporary coefficients for the Trauma Injury Severity Score in New Zealand, TRISS(NZ), and to evaluate their performance at predicting survival against the original TRISS coefficients. Methods – Retrospective cohort study of adults who sustained a serious traumatic injury, and who survived until presentation at Auckland City, Middlemore, Waikato, or North Shore Hospitals between 2002 and 2006. Coefficients were estimated using ordinary and multilevel mixed-effects logistic regression models. Results – 1735 eligible patients were identified, 1672 (96%) injured from a blunt mechanism and 63 (4%) from a penetrating mechanism. For blunt mechanism trauma, 1250 (75%) were male and average age was 38 years (range: 15-94 years). TRISS information was available for 1565 patients of whom 204 (13%) died. Area under the Receiver Operating Characteristic (ROC) curves was 0.901 (95%CI: 0.879-0.923) for the TRISS(NZ) model and 0.890 (95% CI: 0.866-0.913) for TRISS (P<0.001). Insufficient data were available to determine coefficients for penetrating mechanism TRISS(NZ) models. Conclusions – Both TRISS models accurately predicted survival for blunt mechanism trauma. However, TRISS(NZ) coefficients were statistically superior to TRISS coefficients. A strong case exists for replacing TRISS coefficients in the New Zealand benchmarking software with these updated TRISS(NZ) estimates.

Estimating interactive coefficients for analysing interactive failures

Engineering assets are often complex systems. In a complex system, components often have failure interactions which lead to interactive failures. A system with interactive failures may lead to an increased failure probability. Hence, one may have to take the interactive failures into account when designing and maintaining complex engineering systems. To address this issue, Sun et al have developed an analytical model for the interactive failures. In this model, the degree of interaction between two components is represented by interactive coefficients. To use this model for failure analysis, the related interactive coefficients must be estimated. However, methods for estimating the interactive coefficients have not been reported. To fill this gap, this paper presents five methods to estimate the interactive coefficients including probabilistic method; failure data based analysis method; laboratory experimental method; failure interaction mechanism based method; and expert estimation method. Examples are given to demonstrate the applications of the proposed methods. Comparisons among these methods are also presented.

Trauma and Injury Severity Score (TRISS) coefficients 2009 revision

Background: Currently used Trauma and Injury Severity Score (TRISS) coefficients, which measure probability of survival (Ps), were derived from the Major Trauma Outcome Study (MTOS) in 1995 and are now unlikely to be optimal. This study aims to estimate new TRISS coefficients using a contemporary database of injured patients presenting to emergency departments in the United States; and to compare these against the MTOS coefficients.---------- Methods: Data were obtained from the National Trauma Data Bank (NTDB) and the NTDB National Sample Project (NSP). TRISS coefficients were estimated using logistic regression. Separate coefficients were derived from complete case and multistage multiple imputation analyses for each NTDB and NSP dataset. Associated Ps over Injury Severity Score values were graphed and compared by age (adult ≥ 15 years; pediatric < 15 years) and injury mechanism (blunt; penetrating) groups. Area under the Receiver Operating Characteristic curves was used to assess coefficients’ predictive performance.---------- Results: Overall 1,072,033 NTDB and 1,278,563 weighted NSP injury events were included, compared with 23,177 used in the original MTOS analyses. Large differences were seen between results from complete case and imputed analyses. For blunt mechanism and adult penetrating mechanism injuries, there were similarities between coefficients estimated on imputed samples, and marked divergences between associated Ps estimated and those from the MTOS. However, negligible differences existed between area under the receiver operating characteristic curves estimates because the overwhelming majority of patients had minor trauma and survived. For pediatric penetrating mechanism injuries, variability in coefficients was large and Ps estimates unreliable.---------- Conclusions: Imputed NTDB coefficients are recommended as the TRISS coefficients 2009 revision for blunt mechanism and adult penetrating mechanism injuries. Coefficients for pediatric penetrating mechanism injuries could not be reliably estimated.

Stiffness and damping coefficients of 3-axial groove water lubricated bearing using perturbation technique

A Computational fluid dynamics (CFD) approach is used to model fluid flow in a journal bearing with three equi-spaced axial grooves and supplied with water from one end. Water is subjected to both velocity (Couette) & pressure induced (Poiseuille) flow. The working fluid passing through the bearing clearance generates driving force components that may increase the unstable vibration of the rotor. It is important to know the accurate rotor dynamic force component for predicting the instability of rotor bearing systems. In this paper a study has been made to obtain the stiffness and damping coefficients of 3 axial groove bearing using Perturbation technique.

Activity analysis in complicated scenes using DFT coefficients of particle trajectories

Modelling activities in crowded scenes is very challenging as object tracking is not robust in complicated scenes and optical flow does not capture long range motion. We propose a novel approach to analyse activities in crowded scenes using a “bag of particle trajectories”. Particle trajectories are extracted from foreground regions within short video clips using particle video, which estimates long range motion in contrast to optical flow which is only concerned with inter-frame motion. Our applications include temporal video segmentation and anomaly detection, and we perform our evaluation on several real-world datasets containing complicated scenes. We show that our approaches achieve state-of-the-art performance for both tasks.

On the prediction of simultaneous inbreeding coefficients at multiple loci

A new deterministic method for predicting simultaneous inbreeding coefficients at three and four loci is presented. The method involves calculating the conditional probability of IBD (identical by descent) at one locus given IBD at other loci, and multiplying this probability by the prior probability of the latter loci being simultaneously IBD. The conditional probability is obtained applying a novel regression model, and the prior probability from the theory of digenic measures of Weir and Cockerham. The model was validated for a finite monoecious population mating at random, with a constant effective population size, and with or without selfing, and also for an infinite population with a constant intermediate proportion of selfing. We assumed discrete generations. Deterministic predictions were very accurate when compared with simulation results, and robust to alternative forms of implementation. These simultaneous inbreeding coefficients were more sensitive to changes in effective population size than in marker spacing. Extensions to predict simultaneous inbreeding coefficients at more than four loci are now possible.

A comparison of finite difference and finite volume methods for solving the space fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non-classical diffusion or dispersion; that is, not adequately described by the classical theory of Brownian motion and Fick's law. We consider a space fractional advection-dispersion equation based on a fractional Fick's law. The equation involves the Riemann-Liouville fractional derivative which arises from assuming that particles may make large jumps. Finite difference methods for solving this equation have been proposed by Meerschaert and Tadjeran. In the variable coefficient case, the product rule is first applied, and then the Riemann-Liouville fractional derivatives are discretised using standard and shifted Grunwald formulas, depending on the fractional order. In this work, we consider a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Grunwald formulas are used to discretise the fractional derivatives at control volume faces. We compare the two methods for several case studies from the literature, highlighting the convenience of the finite volume approach.

A comparison of finite difference and finite volume methods for solving the space-fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non- classical diffusion or dispersion which is not adequately described by the classical theory of Brownian motion and Fick’s law. We consider a space-fractional advection-dispersion equation based on a fractional Fick’s law. Zhang et al. [Water Resources Research, 43(5)(2007)] considered such an equation with variable coefficients, which they dis- cretised using the finite difference method proposed by Meerschaert and Tadjeran [Journal of Computational and Applied Mathematics, 172(1):65-77 (2004)]. For this method the presence of variable coef- ficients necessitates applying the product rule before discretising the Riemann–Liouville fractional derivatives using standard and shifted Gru ̈nwald formulas, depending on the fractional order. As an alternative, we propose using a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Gru ̈nwald formulas are used to discretise the Riemann–Liouville fractional derivatives at control volume faces, eliminating the need for product rule expansions. We compare the two methods for several case studies, highlighting the convenience of the finite volume approach.